Coherent states, wavelets & their generalizations

This book presents a survey of the theory of coherent states, wavelets, and some of their generalizations, emphasizing mathematical structures. The point of view is that the theories of wavelets and coherent states can both be subsumed into a single mathematical structure. Many concrete examples are discussed in detail, using semisimple Lie groups, relativity groups, and several kinds of wavelets.

Preface.- Introduction.- Canonical Coherent States.- Positive Operator-Valued Measures and Frames.- Some Group Theory.- Hilbert Spaces.- Square Integrable and Holomorphic Kernels.- Covariant Coherent States.- Coherent States from Square Integrable Representations.- Some Examples and Generalizations.- CS of General Semidirect Product Groups.- CS of Product Groups.- Wavelets.- Discrete Wavelet Transforms.- Multidimensional Wavelets.- Wavelets Related to Other G Groups.- The Discretiaztion Problem: Frames Samplin. and all that.- Conclusion.

From the reviews:"The subject of coherent states and/or wavelets (CS-W) is a hot topic for decades. ... Personally I prefer the book under review to many other ones published before. ... It is clearly written, mathematically sound and well illustrated ... . Short but informative historical remarks in the text additionally guide through the literature. The index is useful too. ... I recommend this book to everyone who wishes to learn CS-W, or already works in the area, or just needs a good reference source." (Vladimir V. Kisil, Zentralblatt MATH, Vol. 1064, 2005)